We will later (Section ) describe some lower bounds for finding other subgraphs in the \(\mathsf {CONGEST}\)  model which are based on reductions from 2-party communication complexity problems, and there we will see why these techniques do not give any meaningful lower bound for triangles. Moreover, in the spirit of the aforementioned argument of Drucker, Kuhn, and Oshman [1]}, Eden, Fiat, Fischer, Kuhn, and Oshman [2]} showed that any polynomial lower bound of \(\Omega (n^{\alpha })\)  for some constant \(\alpha \)  for triangle detection in \(\mathsf {CONGEST}\)  would imply major breakthroughs in circuit complexity. This leaves us with another curious gap in our knowledge of triangle finding in this model.
